Question

A)x²-8x=0b)5x²-20=0c)3x²+8x-3=0​

Answer 1

а б и с, по цифрам разберёшься)

Answer 2

To solve these quadratic equations, you can use the quadratic formula, which is given by:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Let's solve each of your quadratic equations:

a) $x^2 - 8x = 0$

In this equation, $a = 1$, $b = -8$, and $c = 0$. Plug these values into the quadratic formula:

$x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(0)}}{2(1)}$

Simplify it:

$x = \frac{8 \pm \sqrt{64}}{2}$

Now, find the two possible solutions:

1. $x = \frac{8 + 8}{2} = \frac{16}{2} = 8$
2. $x = \frac{8 - 8}{2} = \frac{0}{2} = 0$

So, the solutions to the equation $x^2 - 8x = 0$ are $x = 0$ and $x = 8$.

b) $5x^2 - 20 = 0$

In this equation, $a = 5$, $b = 0$, and $c = -20$. Plug these values into the quadratic formula:

$x = \frac{0 \pm \sqrt{0^2 - 4(5)(-20)}}{2(5)}$

Simplify it:

$x = \frac{\pm \sqrt{0 + 400}}{10}$

Now, find the two possible solutions:

1. $x = \frac{0 + 20}{10} = \frac{20}{10} = 2$
2. $x = \frac{0 - 20}{10} = \frac{-20}{10} = -2$

So, the solutions to the equation $5x^2 - 20 = 0$ are $x = -2$ and $x = 2$.

c) $3x^2 + 8x - 3 = 0$

In this equation, $a = 3$, $b = 8$, and $c = -3$. Plug these values into the quadratic formula:

$x = \frac{-8 \pm \sqrt{8^2 - 4(3)(-3)}}{2(3)}$

Simplify it:

$x = \frac{-8 \pm \sqrt{64 + 36}}{6}$

Now, find the two possible solutions:

1. $x = \frac{-8 + \sqrt{100}}{6} = \frac{-8 + 10}{6} = \frac{2}{6} = \frac{1}{3}$
2. $x = \frac{-8 - \sqrt{100}}{6} = \frac{-8 - 10}{6} = \frac{-18}{6} = -3$